File:Venn0001.svg

此SVG文件的PNG预览的大小：384 × 280像素。其他分辨率：320 × 233像素 | 640 × 467像素 | 1,024 × 747像素 | 1,280 × 933像素 | 2,560 × 1,867像素。

原始文件（SVG文件，尺寸为384 × 280像素，文件大小：3 KB）

本文件来自维基共享资源并可能被其他项目使用。其文件描述页上的描述显示在下面。

摘要

描述

English: One of 16 Venn diagrams, representing 2-ary Boolean functions like set operations and logical connectives:

Operations and relations in set theory and logic

∅^c

A = A

A^c

\scriptstyle \cup

B^c

true
^{A ↔ A}

A

\scriptstyle \cup

B

A

\scriptstyle \subseteq

B^c

A

\scriptstyle \Leftrightarrow

A

\scriptstyle \supseteq

B^c

A

\scriptstyle \cup

B^c

¬A

\scriptstyle \lor

¬B
^{A → ¬B}

A

\scriptstyle \Delta

B

A

\scriptstyle \lor

B
^{A ← ¬B}

A^c

\scriptstyle \cup

B

A

\scriptstyle \supseteq

B

A

\scriptstyle \Rightarrow

¬B

A = B^c

A

\scriptstyle \Leftarrow

¬B

A

\scriptstyle \subseteq

B

B^c

A

\scriptstyle \lor

¬B
^{A ← B}

A

\scriptstyle \oplus

B
^{A ↔ ¬B}

A^c

¬A

\scriptstyle \lor

B
^{A → B}

B

B = ∅

A

\scriptstyle \Leftarrow

B

A = ∅^c

A

\scriptstyle \Leftrightarrow

¬B

A = ∅

A

\scriptstyle \Rightarrow

B

B = ∅^c

¬B

A

\scriptstyle \cap

B^c

A

(A

\scriptstyle \Delta

B)^c

¬A

A^c

\scriptstyle \cap

B

\scriptstyle \Leftrightarrow

false

A

\scriptstyle \Leftrightarrow

true

A = B

A

\scriptstyle \Leftrightarrow

false

B

\scriptstyle \Leftrightarrow

true

A

\scriptstyle \land

¬B

A^c

\scriptstyle \cap

B^c

A

\scriptstyle \leftrightarrow

B

A

\scriptstyle \cap

B

¬A

\scriptstyle \land

B

A

\scriptstyle \Leftrightarrow

B

¬A

\scriptstyle \land

¬B

∅

A

\scriptstyle \land

B

A = A^c

false
^{A ↔ ¬A}

A

\scriptstyle \Leftrightarrow

¬A

These sets (statements) have complements (negations).
They are in the opposite position within this matrix.

These relations are statements, and have negations.
They are shown in a separate matrix in the box below.

more relations

The operations, arranged in the same matrix as above. The 2x2 matrices show the same information like the Venn diagrams. (This matrix is similar to this Hasse diagram.) In set theory the Venn diagrams represent the set, which is marked in red.	These 15 relations, except the empty one, are minterms and can be the case. The relations in the files below are disjunctions. The red fields of their 4x4 matrices tell, in which of these cases the relation is true. (Inherently only conjunctions can be the case. Disjunctions are true in several cases.) In set theory the Venn diagrams tell, that there is an element in every red, and there is no element in any black intersection.
Negations of the relations in the matrix on the right. In the Venn diagrams the negation exchanges black and red. In set theory the Venn diagrams tell, that there is an element in one of the red intersections. (The existential quantifications for the red intersections are combined by or. They can be combined by the exclusive or as well.)	Relations like subset and implication, arranged in the same kind of matrix as above. In set theory the Venn diagrams tell, that there is no element in any black intersection.

日期

2008年1月22日

来源

自己的作品

作者

Watchduck

SVG开发

该SVG的源代码为有效代码。

本示意图使用Inkscape创作.

许可协议

此作品不具有版权，属于公有领域，因为其所包含之内容均为公共信息，不包含任何原创内容。

文件历史

点击某个日期/时间查看对应时刻的文件。

	日期/时间	缩⁠略⁠图	大小	用户	备注
当前	2025年1月23日 (四) 22:05		384 × 280（3 KB）	wikimediacommons>Watchduck	correct size

文件用途

以下2个页面使用本文件：

File:Venn0001.svg

摘要

Operations and relations in set theory and logic

许可协议

说明

此文件中描述的项目

描繪內容

資料大小

2,908 字节

高度

280 像素

寬度

384 像素

多媒體型式

image/svg+xml

核對和

a85bb40a017725cd08586a1c770f055653854c0b

文件历史

文件用途

导航菜单

File:Venn0001.svg

摘要

Operations and relations in set theory and logic

许可协议

说明

此文件中描述的项目

描繪內容

資料大小

2,908 字节

高度

280 像素

寬度

384 像素

多媒體型式

image/svg+xml

核對和

a85bb40a017725cd08586a1c770f055653854c0b

文件历史

文件用途

导航菜单

搜索